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Birefringence is a property of certain materials where the refractive index of the material is dependent upon the polarization and direction of propagation of light through it. I recently learned about it while reading a book on lasers.

Reflection and refraction are phenomena that arise from changes in relative permittivity, and they are exactly the same physical concepts as we see in electromagnetic wave propagation through transmission lines. Fundamentally speaking, they are both aspects of wave impedance, and the calculations used in both arenas are identical.

It therefore occurs to me that birefringence is not limited solely to the domain of optics, and we might also observe the behaviour in electronics - perhaps as some sort of transmission line where the characteristic impedance differs depending on the direction of wave propagation through it.

I suspect that a very tiny amount of birefringence is observable in all conductors, e.g. due to variation in crystalline structure within the metal, but I'm more interested in examples where the magnitude of birefringence is significant enough to be a factor worthy of consideration in practical applications.

Are there any significant examples of birefringence's appearance or exploitation within electronics, specifically in the electrical domain rather than the optical domain?

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    \$\begingroup\$ I am baffled by the "opinion based" close vote on this question. Surely the question of whether or not the physical phenomenon of birefringence is observed in the electrical domain is, by the very definition of the word, objective? \$\endgroup\$
    – Polynomial
    Commented Sep 21, 2022 at 12:12
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    \$\begingroup\$ @Andyaka By that second argument one could close almost any question on this site, since new understandings and technologies are always possible, and future developments are a fundamental tenet of the scientific process that should be implicitly assumed. As for whether or not the answer may be a bounded yes (one or two examples given our current understanding and technologies), or an unbounded yes (it's everywhere), or a no - I could not possibly know which it is before receiving an answer, so to argue that this question should be closed because one of those might be the case is a tautology. \$\endgroup\$
    – Polynomial
    Commented Sep 21, 2022 at 12:35
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    \$\begingroup\$ Basically all flexible waveguides are anisotropic if you bend them, so it appears as a nuisance in cabling. I'm not sure of productive uses. In optics, material birefringence is widely used in free space optics (splitters, attenuators, isolators), whereas free space electronic components are not so common due to the longer wavelengths. \$\endgroup\$
    – user1850479
    Commented Sep 21, 2022 at 13:07
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    \$\begingroup\$ @user1850479 Any scenario where birefringence constitutes an electrically relevant phenomenon, whether it be wanted or unwanted, would be of interest to me. \$\endgroup\$
    – Polynomial
    Commented Sep 21, 2022 at 13:41
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    \$\begingroup\$ Unwanted anisotropy shows up in lots of places, especially at high frequencies. PCBs are made of fiberglass and so have birefringence between the fiber axis and perpendicular axes. Bending any waveguide does something similar. For very high frequency interconnects (PCIe 5, USB4, DDR5, etc), a lot of effort goes into manufacturing devices (PCBs, coaxial cables, etc) that have relatively uniform, isotropic properties. \$\endgroup\$
    – user1850479
    Commented Sep 21, 2022 at 14:04

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As @user1850479 mentioned, birefringence is a well-known issue in traces on high-speed PCBs. If you are searching for references, just call it "anisotropy" since that's how the signal integrity literature refers to it. It's also an issue in microstrip patch antennas.

If you want a paper in more depth look at "Pulse propagation on Microstrip transmission-line Using an anisotropic substrate" by Awasthi and Verma at the 2008 International Conference on Recent Advances in Microwave Theory and Applications, or "Modal Analysis of Microstrip Antenna on Fiber Reinforced Anisotropic Substrates" by Yang and Hung in IEEE Transactions on Antennas, vol 57, 792-796, 2009. Those papers have earlier references.

In high speed buried PCB traces, the issue is that you want a dispersionless line to avoid spoiling the rising and falling edges of pules. Dispersionless in turn requires a transverse electromagnetic wave, which in turn requires a homogeneous substrate material.

In circular polarization microstrip patch antennas (e.g. low cost GPS antennas) pure circular polarization (called low axial ratio in antenna specs) is achieved by closely matching the x and y electric dimensions, that is, the dimension in wavelengths should be the same in x and y. Birefringence messes that up, and since the bandwidth of a microstrip patch is only a few percent, it doesn't take much of it to create a problem.

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